What is the population of state A?
I. After an increase in the population of state A by `12%` it becomes `627.20` lakhs.
II. Ratio of population of state A to that of state B is `4:5`.

Options

A. A) only I is sufficient
B. B) Both are required
C. C) only II is sufficient
D. D) None of these

Answer

To determine the population of state A, we need to analyze the two statements provided:

### Step 1: Analyze Statement I
Statement I states that after an increase in the population of state A by 12%, it becomes 627.20 lakhs.

This means that 112% of the original population (which includes the 12% increase) is 627.20 lakhs.

To find the original population (100%), we can set up the equation:
\[ 112\% \text{ of population} = 627.20 \text{ lakhs} \]
This can be expressed mathematically as:
\[ \frac{112}{100} \times \text{Population} = 627.20 \]

### Step 2: Solve for the Original Population
To find the original population, we rearrange the equation:
\[ \text{Population} = \frac{627.20 \times 100}{112} \]

Calculating this gives:
\[ \text{Population} = \frac{62720}{112} = 560 \text{ lakhs} \]

### Step 3: Analyze Statement II
Statement II states that the ratio of the population of state A to that of state B is 4:5.

While this provides a relationship between the populations of states A and B, it does not give us enough information to determine the exact population of state A on its own. Without knowing the population of state B or any additional information, we cannot find the population of state A.

### Conclusion
From the analysis:
- Statement I alone is sufficient to determine the population of state A (560 lakhs).
- Statement II alone is not sufficient to determine the population of state A.

Thus, the answer is that **only Statement I is needed** to find the population of state A.

### Final Answer
The population of state A is **560 lakhs**.

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